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Updated: Apr 29, 2026
10:03
Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
Published on: October 5, 2018
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Conduction-only transport phenomena in compressible bivelocity fluids: diffuse interfaces and Korteweg stresses
1Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA.
Summary
Current diffuse interface theories for fluids are incomplete. Bivelocity hydrodynamics offers a comprehensive framework for diffuse interfaces, including new constitutive equations for Korteweg stress and thermocapillary coefficients.
Area of Science:
- Fluid dynamics
- Continuum mechanics
- Thermodynamics
Background:
- Diffuse interface theories, rooted in van der Waals and Cahn-Hilliard, combine thermodynamics and continuum mechanics.
- Dunn and Serrin established a continuum-thermomechanical basis for Korteweg stresses using an interstitial work-flux.
- Existing theories are considered ad hoc and incomplete due to the lack of an independent volume transport equation.
Purpose of the Study:
- To address the limitations of current diffuse interface theories for compressible fluids.
- To introduce bivelocity hydrodynamics as a rational and comprehensive alternative.
- To derive correct constitutive equations for Korteweg stress and thermocapillary coefficients.
Main Methods:
- Critically analyzing existing diffuse interface theories and their reliance on Helmholtz free-energy and Newtonian mechanics.
- Incorporating an independent volume transport equation, including diffuse volume flux and rate of volume production.
- Applying bivelocity hydrodynamics to develop a comprehensive theory for diffuse interfaces.
Main Results:
- Identified the incompleteness of current diffuse interface theories due to the omission of an independent volume transport equation.
- Established bivelocity hydrodynamics as a rational, non-ad hoc theory for diffuse interfaces in fluids and crystalline solids.
- Derived the correct constitutive equation for Korteweg stress in Newtonian fluids and determined the functional forms of Korteweg's thermocapillary coefficients.
Conclusions:
- Bivelocity hydrodynamics provides a complete and rational framework for diffuse interface theories.
- The study corrects and extends the understanding of Korteweg stresses and thermocapillary coefficients.
- This work offers a more robust theoretical foundation for fluid and solid interface phenomena.
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